dspat: Fits spatial model to distance sampling data

Description

Creates a dspat object by fitting model represented by formula to observations along line transects in a study area with covariates defined for a grid over the entire study area.

Usage

dspat(int.formula=~1, det.formula=~1, study.area, obs, lines, covariates, epsvu=c(1,.01), width=NULL, use.gam=FALSE, show.warnings=FALSE, nclass=NULL)

Arguments

int.formula

formula for model of the point process intensity

det.formula

formula for interaction with distance in the detection process

study.area

owin class for study area

obs

dataframe of observations

lines

dataframe of lines

covariates

dataframe of covariates on a grid in the study area

epsvu

vector of height of pixels(y) and width of pixels(x)

width

full transect width; only needed if it is not specified in lines.df

use.gam

if TRUE uses gam instead of glm for fitting; if formula contains s() use.gam will be set TRUE by default

show.warnings

if TRUE, show the warnings created in building the quadrature.

nclass

number of distance classes for expected/observed counts.

Value

model: output object from ppm
lines.psp: psp line segment process for center lines
transects: list of dataframes specifying polygonal transects
covariate.im: list of covariate images (class im)
study.area: owin class of study area
use.gam: TRUE if gam used and FALSE otherwise

Details

covariates has following structure x - x coordinate of midpoint of grid cell y - y coordinate of midpoint of grid cell ... - any number of covariate

the data are ordered by column from left to right and from bottom to top such that y changes first from smallest to largest. Below are matrices showing y,x and their order 3,1 3,2 3,3 3 6 9 2,1 2,2 2,3 2 5 8 1,1 1,2 1,3 1 4 7

The default for the intensity formula (int.formula) is ~1, a homogeneous Poisson process. Note that what is actually fitted is ~-1+constant where constant is 1 everywhere. This is done to avoid a glitch in vcov.ppm. The detection formula (det.formula) is expressed as a formula that interacts with $ I(-distance^2/2)$. The default of ~1 is a detection function that is constant everywhere. If you use ~-1, it will drop distance which assumes a strip transect with perfect detection within the strip. The variables contained in int.formula must be all contained within covariates because they need to be defined across the entire study area. The variables contained in det.formula can be in covariates or in lines because for prediction of the intensity, distance is set to zero, so these covariates need not be known across the entire survey area.

The value of epsvu[2] is adjusted such that it is an even multiple of width/2 so that the grid points are evenly distributed in the direction of perpendicular distance.

Examples

Run this code


# get example data
data(DSpat.lines)
data(DSpat.obs)
data(DSpat.covariates)
# Fit model with covariates used to create the data
sim.dspat=dspat(~ river + factor(habitat),
                study.area=owin(xrange=c(0,100), yrange=c(0,100)),
                obs=DSpat.obs,lines=DSpat.lines,covariates=DSpat.covariates,
                epsvu=c(4,.1),width=0.4)

# Print
sim.dspat
# Summarize results
summary(sim.dspat)
# Extract coefficients
coef.intensity <- coef(sim.dspat)$intensity
coef.detection <- coef(sim.dspat)$detection
# Extract variance-covariance matrix (inverse information matrix)
J.inv <- vcov(sim.dspat)
# Compute AIC
AIC(sim.dspat)
# Visualize intensity (no. animals per area) and estimate abundance
mu.B <- integrate.intensity(sim.dspat,dimyx=100)
cat('Abundance =       ', round(mu.B$abundance,0), "\n")
dev.new()
plot(mu.B$lambda, col=gray(1-c(1:100)/120), main='Estimated Intensity')
plot(sim.dspat$model$Q$data,add=TRUE)
plot(owin(poly=sim.dspat$transect),add=TRUE)
plot(sim.dspat$lines.psp,lty=2,add=TRUE)

# Compute se and confidence interval for abundance without over-dispersion
mu.B <- integrate.intensity(sim.dspat,se=TRUE,dimyx=100)
cat("Standard Error =  ", round(mu.B$precision$se,0), "\n",
    "95 Percent Conf. Int. =   (", round(mu.B$precision$lcl.95,0), ',',
           round(mu.B$precision$ucl.95,0), ")", "\n")
# Compute se and confidence interval for abundance with over-dispersion estimate
dev.new()
# The rest of the example has been put into a function to speed up package checking; remove # to run
# to run type do.dspat()
do.spat=function()
{
mu.B <- integrate.intensity(sim.dspat,se=TRUE,od=TRUE,reps=30,dimyx=100)
cat("Standard Error (corrected) =     ", round(mu.B$precision.od$se,0), "\n",
    "95 Percent Conf. Int. (corrected) =      (", round(mu.B$precision.od$lcl.95,0),
              ",", round(mu.B$precision.od$ucl.95,0), ")", "\n")
# Fit model with smooth of x and y
sim.dspat=dspat(~ s(x) + s(y),study.area=owin(xrange=c(0,100), yrange=c(0,100)),
                obs=DSpat.obs,lines=DSpat.lines,covariates=DSpat.covariates,
                epsvu=c(1,.01),width=0.4)
AIC(sim.dspat)
# Visualize intensity (no. animals per area) and estimate abundance
mu.B <- integrate.intensity(sim.dspat,dimyx=100,se=TRUE)
cat('Abundance =       ', round(mu.B$abundance,0), "\n")
cat("Standard Error =     ", round(mu.B$precision$se,0), "\n",
    "95 Percent Conf. Int. =      (", round(mu.B$precision$lcl.95,0),
              ",", round(mu.B$precision$ucl.95,0), ")", "\n")
dev.new()
plot(mu.B$lambda, col=gray(1-c(1:100)/120), main='Estimated Intensity')
plot(sim.dspat$model$Q$data,add=TRUE)
plot(owin(poly=sim.dspat$transect),add=TRUE)
plot(sim.dspat$lines.psp,lty=2,add=TRUE)
#
# Fit model with smooth of x and y with interaction
#
sim.dspat=dspat(~ s(x,y),study.area=owin(xrange=c(0,100), yrange=c(0,100)),
                obs=DSpat.obs,lines=DSpat.lines,covariates=DSpat.covariates,
                epsvu=c(1,.01),width=0.4)
AIC(sim.dspat)
# Visualize intensity (no. animals per area) and estimate abundance
mu.B <- integrate.intensity(sim.dspat,dimyx=100,se=TRUE)
cat('Abundance =       ', round(mu.B$abundance,0), "\n")
cat("Standard Error =     ", round(mu.B$precision$se,0), "\n",
    "95 Percent Conf. Int. =      (", round(mu.B$precision$lcl.95,0),
              ",", round(mu.B$precision$ucl.95,0), ")", "\n")
dev.new()
plot(mu.B$lambda, col=gray(1-c(1:100)/120), main='Estimated Intensity')
plot(sim.dspat$model$Q$data,add=TRUE)
plot(owin(poly=sim.dspat$transect),add=TRUE)
plot(sim.dspat$lines.psp,lty=2,add=TRUE)
}